neg. process

I have a question about the negative binomial process.

It is given that $\displaystyle \left(X_{k}\right)_{k=1,2,3,.....} $ is a sequence of geometric random variables
And $\displaystyle S_{k}=X_{1}+.....+X_{k} $ is negative binomial (i,p)
So $\displaystyle \ P\left(S_{i}=k\right) $ a negative binomial distribution (i,p)